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2 How does household portfolio diversification vary with financial sophistication and advice? Hans-Martin von Gaudecker March 22, 2011 Abstract Economic theory suggests that households should invest their financial wealth in a combination of cash and a well-diversified equity portfolio. Yet, many households equity investments are strongly concentrated in a few assets. Attempts to explain this discrepancy have included low levels of cognitive skills and/or financial knowledge; and poor or misguided financial advice. In order to investigate these claims empirically, I construct detailed portfolios for the respondents to a Dutch household survey. The data allow me to estimate the portfolios risk-return properties without resorting to assumptions about characteristics of specific asset classes. Controlling for a large number of covariates, my results show that the combination of low numerical-financial skills and not seeking advice from other persons is strongly associated with the largest losses from underdiversification, whereas financial knowledge does not seem to have much of an effect. JEL codes: D14, D12, G11 Keywords: Household portfolios, diversification, financial literacy, financial advice. Universität Mannheim, Department of Economics; L 7, 3-5; Mannheim; Germany; hmgaudecker[at] uni-mannheim[dot]de; tel Several of the data manipulations and preliminary estimations were performed by Mark Prins for his MSc Thesis at the VU University Amsterdam and in a subsequent research assistantship to the author. Funding from Netspar is gratefully acknowledged. Special thanks to him for an excellent programming job and many fruitful discussions. I appreciate helpful comments received from seminar and conference participants at Frankfurt, at the 2 nd SAVE conference in Deidesheim, and the 2011 Netspar Pension Workshop in Amsterdam, in particular Tabea Bucher-Koenen, Dimitris Georgarakos, Michael Haliassos, Olivia Mitchell, Stephen Zeldes, and Michael Ziegelmeyer. Furthermore, I would like to thank CentERdata for providing the string variables necessary to create the individual return series; Mauro Mastrogiacomo for passing on code to prepare the DHS data; and Maarten van Rooij, Annamaria Lusardi, and Rob Alessie for providing the data and code used to construct the financial literacy scores in van Rooij et al. (forthcoming). 1

3 1 Introduction Going back to at least Markowitz (1952), the canonical model of portfolio choice predicts (a) that households will hold a positive share in risky assets and (b) that the risky component will consist of a well-diversified portfolio, optimising its risk-return characteristics. The earlier empirical studies based on microeconomic data demonstrated that a large fraction of households do not hold any risky assets (e.g. Guiso et al., 2002; Haliassos and Bertaut, 1995; Mankiw and Zeldes, 1991). This finding stimulated the development of a number of theoretical models which can account for this fact. Popular explanations include transaction costs (Vissing-Jørgensen, 2002), background risk (Heaton and Lucas, 2000), or behavioural economic theories (Barberis et al., 2006). See Campbell (2006) for an overview. Largely due to a lack of suitable data, the prediction of a well-diversified portfolio was hardly challenged until recently. Deviations from this recommendation have been documented first by Blume and Friend (1975), but most forcefully by Calvet et al. (2007). The latter employ extraordinarily detailed administrative data, which is only available in very selected countries. The first, minor, contribution of this paper is to demonstrate that their results are replicable to a large degree with survey data when households are asked for the specific items in their portfolios. Theoretical models that predict a low number of stocks in the portfolio are still rare, 1 so underdiversification would generally be considered an investment mistake. The main contribution of this paper is to document the pattern of how losses from underdiversification vary in the population. Compared to the administrative data of Calvet et al. (2007) or Grinblatt et al. (forthcoming), I have much more information about households and individuals, including various measures of financial literacy, the most important source of financial advice, risk attitudes, education, income and wealth. Recently, there has been an increased interest in the lack of financial skills as a driver of poor financial decisions. The output measure has most often been undersaving (Bayer et al., 2009; Cole and Shastry, 2009; Hilgert et al., 2003; Lusardi and Mitchell, 2007a,b), although recent applications include stock market participation (van Rooij et al., forthcoming), overindebtedness (Lusardi and Tufano, 2009), and mortgage delinquency (Gerardi et al., 2010). Very recently, several authors have also connected financial literacy and portfolio diversification (e.g. Bilias et al., 2009; Graham et al., 2009; Guiso and Jappelli, 2009; Kimball and Shumway, 2010), but the available data constrains their choice of portfolio measures. I compare my results to some of those measures and show that there is a substantial benefit to using the more detailed data. My results indicate that the majority of households reaches reasonable levels of diversification. Compared to investing in the benchmark portfolio, the median loss from underdiversification on the financial portfolio is limited to 29 basis points per year. However, the distribution has a fat right tail, where losses become very substantial. The worst outcomes are associated most with the combination of low levels of financial skills and relying on one s own financial judgement (as opposed to seeking advice from professionals or family/friends). This pattern holds regardless of the covariates controlled for. Financial knowledge does not appear to have an effect at any part of the distribution. The pattern suggests that policies targeting 1 Very recently, van Nieuwerburgh and Veldkamp (2010) provided a rationale for low diversification based on information costs. My results show that such an explanation may justify some of the underdiversification seen in the data. However, it is unlikely to stand behind the portfolios incurring the largest losses. The same goes for the beat the Jones argument of Roussanov (2010). 2

4 either numerical-financial skills or the availability of advice may be effective in ameliorating the worst investment outcomes. 2 Data and empirical strategy As discussed in the introduction, recent research has made clear that a significant fraction of households hold widely under-diversified portfolios (Calvet et al., 2007). That and several other studies (Calvet et al., 2009a,b; Massa and Simonov, 2006) are based on administrative records for the Swedish population, where banks were required to report the details of individuals portfolios to the tax authorities. To a lesser extent, the same is true for Finland, where detailed stock holdings and an indicator of mutual fund ownership are available (Grinblatt et al., 2011, forthcoming). To the best of my knowledge, such requirements are not in place anywhere outside Scandinavia and even in Sweden they have ceased to exist with the abolishment of the wealth tax in Since Sweden is unusual in a number of ways most importantly for the topic at hand, a very high stock market participation rate with a stockholder pool that differs markedly from the one in other countries (Christelis et al., 2010a) it is important to find ways for conducting similar analyses in other regions. Furthermore, the use of administrative data limits the range of covariates that can be used to explain portfolio holdings to those collected by the government for administrative purposes. While the number of variables is substantial in Sweden, the content often does not exactly cover what a researcher would like to know. A very popular alternative for investigating individual investment behaviour is to obtain data from discount brokers (Barber and Odean, 2000, 2001; Goetzmann and Kumar, 2008; Hackethal et al., 2011; Ivković et al., 2005, 2008; Korniotis and Kumar, forthcoming; Odean, 1998). An important advantage over the administrative data described before is that these datasets not only contain the portfolio composition at a certain date per year, but all trades in the observation period. Consequently, many of the just-cited studies have focused on the implications of suboptimal trading behaviour for portfolios performance. These datasets are arguably less than optimal to study diversification issues because often only directly held stocks are observed in detail. 2 Furthermore, it is unknown (a) how much of households portfolios the individuals observed accounts cover and (b) to what extent holders of discount brokerage accounts are representative of the population of interest. Tang et al. (2010) pursue a related research strategy in comparing the actual performance of U.S. 401(k) pension plans with the optimal strategy under the investment menu offered by the pension provider. They demonstrate large losses from underdiversification, which almost exclusively stem from participants choices. While the results are suggestive, one cannot know from such data whether at least part of the inefficiencies might be undone outside the tax-deferred accounts: Bergstresser and Poterba (2004) show that half of all individuals who own equity through retirement accounts also own equity outside of these accounts. The most widespread instrument of empirical social science research is the household survey. The U.S. Survey of Consumer Finances has arguably been the most important source of knowledge about household saving and portfolio choice since its inception more than 3 decades ago (see, for example, the literature reviewed in Campbell, 2006). Important 2 For example, Goetzmann and Kumar (2008) use a dummy for mutual fund holdings as an explanatory variable in a regression explaining the underdiversification of the stock portfolio. 3

5 recent contributions focussing on diversification issues include Christelis et al. (forthcoming) or Polkovnichenko (2005). Arguably the main strength of the SCF and general-purpose datasets with a strong module on financial matters 3 is that they contain a wealth of background information in addition to diversification proxies such as the number of directly held stocks, whether the household invests in mutual funds, and asset allocation shares. The main drawback of such surveys is the quality of such diversification measures 4 some investors achieve good diversification results with a low number of stocks while some mutual funds concentrate their investments in very specific sectors. Calvet et al. (2009b, Online Appendix) find that among several potential diversification measures that can be constructed with prototypical survey data, the share of funds in the risky portfolio performs best. Whether the correlation of 0.49 between the fund shares and their favoured measure of diversification (for details on this measure, see Section 2.3 below) is high or low depends on the question at hand. It might well be reasonable as a control variable when the focus is on other questions; but if diversification issues play the central role in an analysis, one would hope for better measures. In this study, I combine several strengths of the various approaches by constructing detailed portfolios for the respondents of the Dutch Central Bank Household Survey (DHS). I describe this survey in the first part of this section, emphasising measures of financial wealth. Linking individual portfolio components to historical return series allows me to calculate diversification statistics that are measured in meaningful economic quantities. After describing the linking procedure and the diversification measures, I sketch a production function framework for explaining investment outcomes. Finally, I outline the variables that serve as inputs into this function, most notably those regarding financial sophistication and advice for financial decision-making. 2.1 Financial wealth variables in the CentERpanel / DHS I use data from the CentERpanel, a Dutch household survey that is administered via the Internet. In order to avoid selection problems due to lack of Internet access, respondents without a computer are equipped with a set-top box for their television set (and with a TV if they do not have one). Respondents are reimbursed for their costs of using the Internet. The panel consists of more than 1,500 households who are representative of the Dutch population in terms of observable characteristics. It has rich background information on important demographic and socio-economic variables. The CentERpanel was the role model for the RAND American Life Panel, which has emerged as another workhorse in the area of household financial decision-making (Hung et al., 2009; Hung and Yoong, 2010; Lusardi and Mitchell, 2007b). The CentERpanel hosts the Dutch Central Bank Household Survey (DHS), which contains particularly detailed information on financial matters. For this reason, it has been used extensively to describe the portfolio choice behaviour of Dutch households, excellent examples are Alessie et al. (2002, 2004, 2006); Dimmock and Kouwenberg (2010); Korniotis and Kumar (forthcoming). My analysis is cross-sectional, but in order to increase the sample size I make 3 Some important examples are the HRS or PSID in the U.S. or the SHARE, ELSA, or ECHP datasets in Europe. Bilias et al. (2010); Christelis et al. (2010a,b); Juster et al. (1999); or Lusardi and Mitchell (2007a) are some exemplary studies using and describing these datasets for related questions. 4 This characteristic is shared by other questionnaire-type approaches that I am aware of, such as tailormade surveys (Kimball and Shumway, 2010), commercial investor surveys (Graham et al., 2009), or hybrids thereof (Guiso and Jappelli, 2006, 2009). 4

6 use of the 2005 and 2006 waves, which contain information on the financial portfolios at the end of the previous year. Because of this, I label them with the years 2004 and 2005 in the remainder of the paper. Table A.1 in the Appendix contains an overview of the relevant asset and debt categories. The 35 entries in the first column are clearly too many to analyse for my purposes and the remaining columns show how I aggregate them into manageable numbers. The most important distinctions are in the upper part of the columns labelled Level 2, differentiating between risky and safe financial assets, and Level 1, which breaks up risky financial assets into three categories: Mutual funds, directly held stocks, and bonds and options. Throughout the analysis, I exclude households with less than 1,000 Euros in financial assets (8.6% of the sample), leaving 2,661 observations on 1,607 households. Figure 1: Ownership rates of and fractions invested in risky assets, by total net worth Ownership of risky financial assets Fraction of risky assets in financial assets Ownership rate Fraction invested Quintile of total net worth Quintile of total net worth Ownership rate All households Conditional on ownership Source: CentERpanel, own calculations. Figure 1 shows risky asset ownership along with unconditional and conditional shares by total net worth. 5 The left panel shows the standard pattern of rising ownership rates in wealth (Guiso et al., 2002), starting from about 13% in the lowest wealth quintile to more than 50% in the highest wealth quintile. As usual, the rise is most pronounced in the highest wealth class. A similar pattern can be seen for the shares invested in risky assets, when averaging over all households, including the non-participants. These rise from 6% in the lowest wealth quintile over 10-11% in the upper-middle quintiles to 24% in the highest. The second line in the right panel reveals that this pattern is mostly driven by ownership rates. Conditional on ownership, risky asset holdings follow a U-shaped pattern with 45% in the two extreme quintiles and 34-36% in the middle quantiles. This contrasts with the pattern of a steep wealth gradient in the risky asset share among participants in Sweden (Calvet et al., 2007, 2009b) and highlights the importance of establishing results along those studies lines for other countries. 2.2 Detailed portfolio components A unique feature of the dataset is that individuals are not only asked for the number of stocks and mutual funds they posses, but also to report the names and quantities held in each 5 Total net worth is defined as total assets minus total debt in the last column of Table A.1. 5

7 of those. 6 In particular, they are asked for the details of their 10 (5, 5) largest positions of stocks (mutual funds, growth funds 7 ). These three items make up the largest share of all risky assets, which furthermore consist of company or mortgage bonds and options (see Table A.1 for details). Table 1: Descriptive statistics on coverage of risky portfolio by components with time series Variable name # raw # obs Mean p 5 Median p 95 (1) Total number of households (2) Owners of risky financial assets (3) Owners of shares/funds (4) Raw report of individual items (5) Raw report (hh. in final sample) (6) Matched report of individual items (7) Fraction of shares/funds covered (8) Fraction of risky fin. assets covered (9) Fraction of quantities imputed (10) Length of time series of returns (11) Total expense ratio, mutual funds Source: CentERpanel, Datastream, Euroinvestor, own calculations. Numbers in column # raw refer to all observations, those in column # obs are adjusted for clustering at the household level, as are the remaining statistics. In the case of the time series of asset returns, the number of observations refers to the number of different assets. Returns are observed at a monthly frequency. The total expense ratio is expressed as an annual percentage of the asset value. The second and third row of Table 1 reveal that of the 528 households who own any risky financial assets, 5% do not own any shares or mutual funds, but only bonds or options. Only two of the remaining households did not provide the names of any of their assets. Several reports were difficult to interpret, leaving 408 different households for whom I could match return series to the larger part of the portfolios components. Row 5 in Table 1 shows that the mean household in the final sample holds 3.7 different items. These numbers are close to those found for the U.S. (e.g. Bilias et al., 2009; Polkovnichenko, 2005) or Sweden (Calvet et al., 2007). The next row shows that I can match close to 3 items on average to historical returns on Datastream and Euroinvestor (not all funds were available on Datastream). The true rate of matches is even higher than the 80% implied by these numbers because in some households, multiple individuals answer the questionnaires and name the same portfolio items. These are 6 The names of individual stocks and mutual funds are not part of the data that is available by default. They may be obtained from CentERdata for a small administrative charge. 7 Growth funds are essentially the same as mutual funds, except for the fact that they reinvest any dividends and interest they receive from their investments. The distinction is made in the questionnaire due to different tax treatments. I do not maintain this distinction and refer to both as mutual funds. 6

8 consolidated in row 6, but not in rows 4 or 5. A similarly positive picture emerges when inspecting the fraction of assets covered by the portfolio components for which a return series is available. The average coverage rate is about 90% with a very left-skewed distribution the median is at 98.9%. Adding bonds and options to the denominator reduces average rates by 5 percentage points and only affects the lower tail of the distribution. In the analysis below, I assume that the unobserved part of the risky portfolio behaves the same way as the observed part and exclude households with coverage rates below 30%, having checked robustness to various levels. Some individuals stated the name of a portfolio component, but did not provide information on the amount held. I imputed this information by assuming that the difference between total portfolio holdings and portfolio holdings attributable to specific assets is equally distributed among all reported assets. This implies that the coverage figures mentioned before are potentially overstated. However, row 9 of Table 1 reveals that this affects only 8% of the portfolio balances, and that it is concentrated among much less than half of all households. Furthermore, half of those who do not provide quantity information on an individual portfolio component have only this one item in their portfolio. Hence, no bias of the diversification results, which are independent of portfolio size, would arise from these households. The bottom part of Table 1 shows that households reported ownership of 269 different assets; of which 170 are mutual funds and 99 are shares. I use the maximum available period for the returns from January 1990 to June 2009, or 235 months, for the analysis. Several assets are observed for shorter periods of time, leading to an average (median) of 138 (128) months. Calvet et al. (2007) abstract from mutual fund fees in their main analysis and explore the robustness of their result to incorporating the exact mutual fund fees for the 10 most popular mutual funds and applying average fees to the rest. I take the opposite path, incorporating mutual fund fees in the main part of the paper and checking robustness to excluding them. I could find information on the fees that 140 of these charge via Morningstar or a fund s prospectus. For another 20 mutual funds, I assigned the fee of similar funds managed by the same company. I imputed the fees for the remaining 10 funds from the distribution of available fees. The last line of Table 1 shows that fees are in the usual range with an annual average of 130 basis points. In the estimations which contain mutual fund fees, I subtract 30 basis points from the benchmark index, which approximates the fees charged by index funds replicating common benchmarks. 2.3 Construction of diversification measures In order to reduce the return series data to single measures of portfolio efficiency, I follow the strategy of Calvet et al. (2007) rather closely and merely sketch it here in order to keep the paper self-contained. The interested reader is referred to Calvet et al. (2007), including the corresponding Online Appendix, for further details. In a first step, I decompose total portfolio risk into a systematic and an idiosyncratic component. All returns are framed as excess returns over the risk-free rate, which is approximated by the money market rate. The portfolio risk decomposition is based on a regression of the household portfolio s excess return r e h,t on a benchmark s excess return re b,t : r e h,t = α h + β h r e b,t + ε h,t I take the MSCI Europe index as the benchmark, the results are robust to using the excess returns of the AEX or the (unhedged) MSCI World Index instead. The decomposition of the 7

9 household s total portfolio risk σ 2 h into a systematic σ2 b and an idiosyncratic σ2 h,idios. component is then given by: (1) σ 2 h = β2 h σ2 b + σ2 h,idios. The advantage of this decomposition is that it is purely statistical, i.e. it does not involve any assumptions about asset pricing. The main drawback is that while a large amount of idiosyncratic risk-taking is a sign of inefficient investing, its magnitude is difficult to interpret. Constructing diversification measures with a meaningful scale requires an estimate of expected returns. Directly estimating expected returns in each dataset would be problematic because of the short return histories for some assets; and because the time series cover different time spans. 8 Again, I follow Calvet et al. (2007) and assume that assets are priced according to a CAPM, where I take the MSCI Europe to proxy the efficient market portfolio. This choice seems natural for a member of the Eurozone. Net of the 30 basis points annual fee, the benchmark has an annual excess return µ b = 5.75% over the 1983-July 2009 period. Along with the standard deviation σ b = 16.7% this leads to a Sharpe ratio S b = µ b /σ b of 35%. Imposing the CAPM leads to the following regression for all assets a = 1, 2, : r e a,t = β a r e b,t + ε a,t. Given the betas of all assets and the portfolio weights for each household, it is straightforward to calculate the expected returns µ h of the household portfolios. A first measure of diversification loss is the relative Sharpe ratio loss: (2) RSL h = 1 S h S b The relative Sharpe ratio loss relates the Sharpe ratio of the household portfolio to that of the benchmark. It equals zero for an efficient portfolio and one for a portfolio where all risk is idiosyncratic. While the relative Sharpe ratio loss has a number of attractive features (see Calvet et al., 2007), its usefulness is confined to risky assets. A poorly diversified risky portfolio will not lead an investor far astray from the efficient frontier if the share in risky assets is sufficiently low. The independence of RSL h of the risky asset share thus is not necessarily desirable. Calvet et al. (2007) therefore define the return loss, which is the average return a household loses by not choosing a position on the efficient frontier with the same level of risk. I skip its derivation and directly report a (slightly simplified) version that is useful for decomposing it into various components: ( ) RSLh (3) RL h = µ b ω h β h 1 RSL h The return loss of the household portfolio is the product of the expected excess return on the market portfolio (which does not vary in the population), the risky asset share ω h, the beta, 8 To see this, assume that one observes two assets with identical moments. Data for the first is available in the period and for the second from 2002 to The first asset would likely have a much lower estimated alpha because the market conditions were worse during the earlier period. Pricing assets via the CAPM avoids this problem as long as the correlation with the index does not change with market conditions. 8

10 and a nonlinear transformation of the relative Sharpe ratio loss. 9 In the mean-variance plane, the return loss is the vertical distance between the efficient frontier and the location of the household portfolio. 2.4 An investment production function One of the big advantages of the CentERpanel/DHS data is that it allows, for the first time, to relate detailed diversification outcomes to covariates that are not typically available in administrative data. For example, the Swedish administrative data of Calvet et al. (2007, 2009b) contain measures of wealth, income, employment, age, household size, education, and immigration status. One of their main findings is that wealthier households invest both more aggressively and more efficiently. The data do not allow to discern whether this is because these households are able to buy better advice; or whether they take better financial decisions by themselves. The policy conclusions would be very different: In the former case, one would target the supply of investment advice. In case investor sophistication is the key, financial education programs could be of help (Tang et al., 2010). In order to clarify concepts, it is useful to think of the investment process in terms of a simple production function. The output is a measure of efficient investment, e.g. one of those considered in the previous subsection. A certainly non-exhaustive list of important inputs identified in the literature are financial literacy/knowledge, cognitive abilities and education, the source of financial advice, risk aversion, age, gender, and several others described below. I approximate the production function by a linear equation (4) Y = X b + u. The investment outcome Y is observed and relevant for the household as a whole, but many of the inputs in the vector X concern individuals. The DHS contains a variable asking about who takes financial decisions in the household on a five point-scale. If both partners agree on a financial decider, I use the inputs for this person. In case of ties (e.g. both partners stating that they have equal say), I use the inputs from the member identified as the household head. The results of Smith et al. (2010) provide some evidence that this approach is sensible. Analysing the correlation between cognitive skills and various economic outcomes for older households, separately for each partner, they show that numeracy of the financial respondent in the HRS data is by far the most important correlate. Previewing the results, we shall see that the diversification loss is close to negligible for a large part of its distribution. However, similar to the Swedish case, losses become rather high in the upper tail. For this reason, I do not only estimate Equation (4) by OLS, but also by means of quantile regressions. An additional benefit of quantile regression is that it provides a direct way to incorporate non-participants in the estimations, provided that the diversification measure is well-defined for non-participants. This is the case for the return loss (3): ω h = 0 or RSL h = 0 imply RL h = 0. Note that the quantile under consideration needs to be strictly positive for all population groups, otherwise the estimator is not well defined. The typical way of including non-participants in a least squares regression would be to model (4) as a two-part process of first deciding whether to invest in risky assets and then 9 The value of RSL h 1 RSL h to zero. I therefore winsorise becomes extremely high if the expected return on a household s portfolio µ h is close RSL h 1 RSL h in the decomposition exercises below. 9

11 how to invest in them (see Pohlmeier and Ulrich (1995) for such a model in another context and Calvet et al. (2007) for an application to portfolio choice). Given that the participation decision has been studied extensively, including with the very data used here (van Rooij et al., forthcoming), such an approach seems to be an unnecessary complication. My analysis identifies subgroups of the population who are at an increased risk of obtaining inferior investment outcomes. It does not without further assumption follow that changing a covariate would lead to a change in Y corresponding to b. Nevertheless, the analysis is an important improvement over the state of the art because it permits to identify conditional relationships. For example, in a related contribution Korniotis and Kumar (2009) first regress cognitive skills in an auxiliary dataset on a number of covariates. They then use the estimated coefficients to predict a smartness score in the dataset containing investment outcomes. Such a procedure only permits the estimation of the bivariate relationship between smartness and investment outcomes and does not allow for separate effects of covariates entering the index. The analysis of Grinblatt et al. (forthcoming) shows the relation between a measure of cognitive skills and some measures of diversification for Finnish males; but the authors can neither condition on education at the individual level nor disentangle whether part of the relationship is mediated through financial advice. 2.5 Inputs to investment production As discussed in the introduction, there has been a huge upsurge in studies that aim to measure the individual skills that enter the right hand side of (4). One reason for using the 2004 and 2005 portfolio data is that at that point in time, Maarten van Rooij, Annamaria Lusardi, and Rob Alessie fielded a battery of questions aimed at estimating respondents financial literacy. The data form the basis of van Rooij et al. (forthcoming) and the authors kindly provided me with data and code. The questions are similar to those in Lusardi and Mitchell (2007b), they are discussed in detail and compared to other measures in Hung et al. (2009). A first set of questions, coined basic financial literacy, contains 5 quiz-like simple math problems. A good example is the numeracy question: Suppose you had e100 in a savings account and the interest rate was 2% per year. After 5 years, how much do you think you would have in the account if you left the money to grow? (i) More than e102; (ii) Exactly e102; (iii) Less than e102; (iv) Do not know; (v) Refusal. Table A.2 in the Appendix shows that 95% of respondents correctly answer this question. The other questions have a similar structure of relatively simple math problems, but correct response rates are lower. Similar to van Rooij et al. (forthcoming), I assume that a single factor is underlying the five questions and normalise this factor to have zero mean and unit variance. The only difference is how I treat Do not know and Refusal answers. Instead of coding another variable, which will have a complicated correlation structure with the substantive answer, I assign those answers the probability of a random guess being correct, e.g. 1/3 for the question above. This can be rationalised by a linear probability model and would be exactly correct if all factor loadings were equal to each other. In the present case, it will be a reasonable approximation. All results are robust to using the exact procedure of van Rooij et al. (forthcoming). The basic financial literacy measures whether individuals possess the necessary cognitive abilities to perform simple numerical computations, which will be important for informed financial decision-making. Indeed, the survey instrument resembles to some extent the numeracy component of the cognitive ability score used in Christelis et al. (2010b) to explain stockholding. The first row of Table 2 shows 10

12 that participants in risky asset markets have a significantly higher basic financial literacy score, confirming one of the main results of van Rooij et al. (forthcoming) and Christelis et al. (2010b). The distribution of the index is left-skewed since 45% of respondents in the entire sample answer all questions correctly, leading to a maximum index value of The second part of the financial literacy module, termed advanced financial literacy, consists of questions relating to knowledge of financial instruments and concepts. For example, the following question asks about the diversification properties of stocks and mutual funds: Buying a company stock usually provides a safer return than a stock mutual fund. True or false? (i) True; (ii) False; (iii) Do not know; (iv) Refusal. Only two thirds of all respondents give the correct answer, but three quarters of those who participate in risky asset markets. The advanced financial literacy index, constructed in the same way as the basic literacy index, also takes on higher values on average for holders of risky assets (see row 2 in Table 2) again as in van Rooij et al. (forthcoming). Conceptually, these financial knowledge questions might be more problematic as inputs in (4) than the basic math skills in the basic module. The reason is that they may be largely shaped by investor experience one would expect an increase in the probability of a correct answer to the example question for somebody who has monitored the evolution of stock and mutual fund returns in his or her portfolio for a while. This is less problematic for analysing efficiency of the risky portfolio than for studying the participation decision, but it remains a concern. The same comment applies to self-assessed financial knowledge, which is the third variable aimed at measuring financial literacy. I dichotomise the four-point rating into a dummy variable, which equals one for 19% (28%) of all households (participants in risky asset markets). Abstracting from agency problems and potential costs, rational households who realise their lack of investment skills would seek external help. 10 The most important source of financial advice is directly asked for in the DHS questionnaire. The second part of Table 2 shows that about a quarter of respondents seek help from professional advisors and that another quarter rely upon the advice of family and friends. The remaining half is made up of a number of categories: Newspapers; financial magazines; guides; books; brochures from the bank or mortgage advisor; advertisements; financial computer programs; the Internet; other. I label the aggregate category reliance on own financial judgement. 11 Their percentage rises among participants in risky asset markets, entirely at the expense of those who turn to their friends and family for financial advice. It is especially interesting to compare the level of financial literacy among the different groups of advice-seeking. Among all respondents, it is significantly lower among those who ask their friends and family compared to any of the two other groups. The same pattern remains for those with risky assets, although the sample size compromises statistical significance. The remaining inputs to the production function are additional controls which serve to sharpen the interpretation of the financial literacy and advice variables. First, the financial literacy variables could merely be an approximation for education if it was not controlled for. Another angle to look at the relation is that to extent that education signals cognitive abilities, one would like to know whether specific (i.e. the basic literacy index) or general 10 Hackethal et al. (2011) show that professional advice not necessarily leads to better outcomes, however. 11 It is debatable whether those who cite brochures from financial institutions as their most important source of advice should rather be added to the category of professional financial advisors. Presumably, a financial institution s advisors and brochures would recommend similar investment strategies. I prefer the classification I chose because brochures seem to focus on advertising specific investments, while advisors would (hopefully) make recommendations based on the entire portfolio. In any case, all results survive a reclassification. 11

13 Table 2: Descriptive statistics on the covariates Variable name Entire sample Portf. returns avail. Mean Std. dev. Mean Std. dev. Basic fin. literacy index Advanced fin. literacy index High self-rated fin. knowledge Financial advice: Professionals Financial advice: Family/friends Financial advice: Own judgement Prof. advice bas. literacy Advice fam./friends bas. literacy Own fin. jugdement bas. literacy No/elementary/secondary education Higher vocal education Academic education Age Age Age Female High tolerance for risky investm Household size Degree of urbanisation Net annual household income 31,711 37,499 40,174 63,195 Log net household income Value of total financial assets 41,513 76,736 84, ,436 Log financial assets Value of total non-financial assets 173, , , ,589 Log total non-fin. assets Value of total debt 55,242 82,810 66,270 91,551 Log total debt Source: CentERpanel, own calculations. All statistics are adjusted for sampling weights, standard deviations of dummy variables are not shown. Variables relating to individuals rather than the household (i.e. all variables except for the last section of the table) are for the financial decider, as defined in Section 2.4. The number of observations where the covariates for the preferred specification (all covariates) are present is 958 (798) for the entire sample and 270 (238) for participants in risky asset markets with detailed portfolio information. For most covariates, the number is much closer to the relevant figures reported in column # obs of Table 1. The interaction terms in the third part of the table give averages of financial literacy within each category of financial advice. 12

14 abilities matter more. I include education in three categories and as expected, it is higher among those with risky assets in their portfolio. Second, cognitive functioning declines with age. However, age may have a positive effect on investor performance through experience (Korniotis and Kumar, forthcoming). Third, cognitive abilities have been shown to correlate with risk aversion (Dohmen et al., 2010). On average, women are more risk averse than men (Croson and Gneezy, 2009), so I include a gender dummy. Furthermore, I use a measure of willingness to take financial risks derived from the degree of agreement with six different statements, each measured on a 7-point scale (e.g. It is more important to have a safe investment with guaranteed returns than taking risk. Totally disagree / Disagree / Partly disagree / Neither agree or disagree / Partly agree / Agree / Totally agree). I add up the answers and standardise the resulting variable to have mean zero and unit variance. The bivariate correlations with risky asset holdings both go in the expected direction, see Table 2 once more. Including these variables in the regression has the drawback of reducing the sample size by about 15%. Hence, I do not include the risk aversion measures in my preferred specification and relegate the tables with added variables to the Appendix. In order to compare my results to those of Calvet et al. (2007), I furthermore include measures of household size, the degree of urbanisation, household income, wealth, and liabilities in various additional specifications. The reason for not incorporating these variables in my standard specification is that their interpretation in the production function framework (4) is not obvious. Almost all explanations would go through abilities (e.g. smart individuals would have higher labour earnings and better investment outcomes) or financial advice (e.g. for rich households professional advice might be cheaper relative to asset volume). Again, I discuss the results in the text and all corresponding tables can be found in the Appendix. 3 Results 3.1 The distribution of efficiency measures For all participants in risky asset markets, Figure 2 contains plots of several measures for each quintile of the distribution of total portfolio risk, as inferred from equation (1). Shown in the left panel, total portfolio risk rises from less than 10% annually in the lowest quintile to almost 40% in the top quintile, with the most pronounced rise at the top. The systematic component moves almost in parallel for the first three quintiles, only then its slope becomes much flatter. Accordingly, the idiosyncratic component shows its steepest increase at the top of the portfolio risk distribution, suggesting that inefficient investing is by far the strongest there. The numbers are remarkably close to those found by Calvet et al. (2007) for Swedish households they report 11% (19.5%, 36.4%) at the 10 th (50 th, 90 th ) percentiles for total portfolio risk. 12 They also find the same U-shaped pattern for the idiosyncratic risk share displayed in the right panel, again with similar magnitudes. In both countries, the high values at the lower end of the distribution are driven by bond mutual funds, which display a low correlation with the benchmark index. This is also reflected in the average beta coefficient inferred from (1), which rises strongly in total portfolio risk. Again, the magnitudes are very close to those reported in Calvet et al. (2007). 12 Given the huge sample size, Calvet et al. (2007) calculate averages around specific percentiles, which enables them to go much further into the tails of the distribution. I compare their reports for the midpoint of quintiles to the quintile-specific averages calculated in my analysis. 13

15 Figure 2: Portfolio risk components by quintile of total portfolio risk Average annualised risk (%) Quintile of total risk in risky portfolio Average share of idiosyncratic risk Quintile of total risk in risky portfolio Average beta coefficient Total portfolio risk Idiosyncratic portfolio risk Systematic portfolio risk Share of idiosyncratic portfolio risk Beta coefficient of portfolio (unrestricted estimate) Source: CentERpanel, Datastream, Euroinvestor, own calculations. See Section 2.3 for computational details. In order to get an understanding of the basic characteristics of household portfolios, it is useful to plot them in the mean-variance plane. Panel A of Figure 3 does this for the pure stock portfolios and reveals a picture of strong underdiversification, which is similar to the findings of Calvet et al. (2007) for Sweden and Goetzmann and Kumar (2008) for the U.S.. The mutual fund component of households portfolios appears much better diversified, even though the CAPM is applied after subtracting mutual fund fees. The major part of the distribution lines up right below the efficient frontier (Panel B of Figure 3). Nevertheless, a substantial fraction of mutual funds perform significantly worse than the market portfolio, conditional on the level of risk. Panel C contains the aggregate of stocks and mutual funds and shows that many households reduce the risk of their stock portfolios by additionally investing in mutual funds (of all risky asset owners, 55% only own mutual funds, 18% only own stocks, and 26% own both). The picture is yet more positive when holdings of safe assets are taken into account in Panel D of Figure 3. Relatively few outliers with severe losses are left at high levels of risk, but there is a number of households with a portfolio that is 1-2 percentage points below the efficient frontier at relatively low levels of risk. Diversification losses of this magnitude will be substantial when accumulated over the life-cycle (Calvet et al., 2007; Tang et al., 2010). In order to allow for an easier interpretation and to perform quantitative analyses, it is useful to reduce the 2-dimensional information in Figure 3 to a single dimension. This is the purpose of the relative Sharpe ratio loss (2) and the return loss (3) presented in Section 2.4. Their quintile-specific values are plotted in Figure 4. The relative Sharpe ratio loss, shown in the left panel, is limited to far less than 20% in the bottom three quintiles, before reaching 27% and 64% in the upper quintiles. Again, this pattern mirrors the findings of Calvet et al. (2007) very closely: Most households largely avoid inefficient risk-taking, but almost two thirds of all the risk the average household in the top quintile takes remains uncompensated. The right panel of Figure 4 contains various measures of return loss. The solid black line just considers the risky portfolio, i.e. it is the vertical distance between the location of a household in Panel C of Figure 3 and the efficient frontier. Put differently, the risky asset share ω h in (3) is set to one. The average return households lose on their risky portfolio compared to an efficient investment equals 180 basis points per year, which is just above the number reported by Calvet et al. (2007) for the unhedged world index as the benchmark. It 14

17 is below 100 basis points for the bottom three quintiles and 585 basis points in the highest. These return losses are far lower when the entire portfolio is taken as the basis again, they are very limited for the first four quintiles (56 basis points in the fourth), but reach the substantial amount of more than 2% in the highest quintile. The average is about 59 basis points, substantially less than the 180 basis points for the risky portfolio multiplied with the risky asset share of.39 (see Figure 1). This implies a negative covariance between the risky asset share and the losses from underdiversification multiplied with the household portfolio s beta. 13 This illustrates the limited usefulness of the relative Sharpe ratio loss for assessing the diversification losses incurred on the entire portfolio on average, those with higher values of RSL h have a smaller share in risky assets, so the losses are less important for them. Finally, the third line in the right panel of Figure 4 demonstrates that, again as in Sweden, the losses are by no means negligible in monetary terms for substantial parts of the population. Relative Sharpe ratio loss of portfolio Figure 4: Mean-variance measures of diversification losses. Relative Sharpe ratio loss Annual return loss (%) Return loss Return loss, percentage of risky assets Return loss, percentage of financial assets Return loss, Euros Annual return loss (Euros) Quintile of relative Sharpe ratio loss Quintile of each variable s distribution Source: CentERpanel, Datastream, Euroinvestor, own calculations. Finally, I plot the various components of the return loss as exemplified by the righthand-side of (3) by its quintiles: The fraction in risky assets ω h, the beta coefficient on the RSL household portfolio, and the transformation of the relative Sharpe ratio loss h 1 RSL h. Of course, the different components do not add up due to Jensen s inequality, so the graphical illustration does not qualify as a decomposition. Nevertheless, it remains useful to get a rough idea of the underlying mechanisms. The beta coefficient rises almost linearly over the quintiles, so inefficient and efficient risk-taking at least go hand in hand on average. The risky asset share increases quickly until the middle of the return loss distribution and modestly afterwards. The diversification loss is fairly constant in the lower quintiles (implying relative Sharpe ratio losses between 24% and 30%) and increases strongly in the top quintile (implied RSL h =.48). Compared to the lower quintiles, the prime driving force behind the highest return losses thus seems to be uncompensated risk taking. 3.2 How do investment outcomes vary in the population? The previous section has shown that the descriptive results of Calvet et al. (2007) can be replicated to a large extent for another country and, more relevantly, on a dataset that is 13 This finding is confirmed by statistical analysis; and it is also true for the covariance between the relative Sharpe ratio loss and ω h. 16

18 Figure 5: Return loss and its components by quintile Return loss Remaining measures Return loss quintile Return loss Beta coefficient Fraction in risky assets Diversification loss Source: CentERpanel, Datastream, Euroinvestor, own calculations. See Section 2.3 for computational details. fairly easy to collect anywhere. While this is an important step, the big advantage of the CentERpanel data is the availability of inputs to the investment production function (4) that have been of particular interest in the literature. Figure 6 once more plots the quintile-specific averages of the return loss, adding non-participants in risky asset markets (for whom RL h = 0 RSL h 1 RSL h since w h = 0 and = 0). For each return loss quintile, the figure furthermore adds the average values of the basic financial literacy index and the share of households relying on their own financial judgement. The financial literacy index shows an inverse U-shaped pattern it is lowest for the non-participants (previously shown by van Rooij et al. (forthcoming) and Christelis et al. (2010b)), rises monotonously until the fourth return loss quintile, before dropping to its second-lowest value in the top quintile. In conjunction with the fact that diversification losses seem to be the driving force behind the largest return losses (Figure 5), this suggests that low investment skills may play an important role in determining the worst outcomes. The same inverse U-shaped pattern is found for the amount of idiosyncratic risk or the relative Sharpe ratio loss, see Figure B.1 in the Appendix. The fraction of individuals relying on their own financial judgements is generally rising in the return loss, although the high value in the second quintile is an exception to the rule. While the bivariate relations are suggestive, a more formal analysis is required to shed light on potential mechanisms. The first column of Table 3 shows the results for an OLS regression of my preferred set of covariates on the sample of participants. The first three rows, containing the basic financial literacy index, the advice variable, and their interaction, already contain the basic result of my analysis. 14 Financial literacy does not have an effect for those who seek external advice the coefficient in the first row is close to zero (2.4 basis points per year) and precisely estimated (the 95% confidence interval ranges from -7.2bp to 12bp). The dummy for deciding on the basis of self-collected information takes on a large and significantly positive value those relying on their own judgement with a financial literacy score of zero on average incur a return loss that is 48 basis points higher than those who rely on external advice. The interaction term shows that this effect is much worse for those with negative values of the financial literacy index and that it almost exactly cancels out for those who achieve the highest financial literacy score. These households are estimated to incur an insignificant extra return 14 The other financial literacy measures did not turn out to have an effect and results for the two left-out groups of financial advice were very similar. More extended specifications are discussed below. 17

19 Figure 6: Financial literacy, financial advice, and diversification losses Return loss, percentage of fin. assets Return loss (%) NP Return loss quintile Remaining measures Return loss (%) Financial advice: Own judgement Basic fin. literacy index Source: CentERpanel, Datastream, Euroinvestor, own calculations. See Section 2.3 for computational details. The return loss quintile value NP stands for non-participants. loss of 48.4bp 73.7bp.63 = 1.9bp on average, compared to those seeking advice from professionals or family/friends with the same level of financial literacy. The coefficients on all other covariates are insignificant and much smaller than those for financial literacy and advice. The results of the quantile regressions shown in the remaining columns of Table 3 are yet more interesting because they show that the averages are entirely driven by effects in the top third of the return loss distribution. None of the percentiles varies much with the level of financial literacy among those seeking external advice. All else equal, the 90 th percentile of the return loss is 148 basis points higher among those who rely on their own financial judgement and have a financial literacy index of zero. Again, the effect becomes much worse for negative values of the financial literacy index and reduces to 40bp for those with the maximum financial literacy score. The same pattern holds for the 70 th percentile, although the magnitudes are substantially smaller. The variation of the coefficients across the quantiles is significant because it shows that (a) most households achieve reasonable investment outcomes regardless of their characteristics and (b) the worst outcomes are concentrated among those who neither seek advice from other individuals nor have a high level of numerical skills. Finally, one should note that there appears to be an age effect that is hidden in the OLS estimates. Return losses are significantly higher around the middle of the distribution for the oldest age group (age 65+) and there is a large negative coefficient for the 90 th percentile, although it is not significant. The same pattern prevails in the middle age group, but all coefficients are insignificant. The coefficients on education are either tiny or point in the expected direction with none of them being significant. Last, females incur larger return losses at the higher quintiles, although they are significant only at one quantile. The estimates reported in Table 3 are valid for the sample of participants in risky asset markets, but they may be different in the general population. To see this, assume there are two groups in the population. One group s members mostly stay out of risky assets and the remaining members invest very inefficiently. The second group fully participates and invests quite efficiently. Conditioning on participation will lead to all quantiles being higher for the 18

20 Table 3: Contributors to return loss OLS p 10 p 30 p 50 p 70 p 90 Basic fin. literacy index (0.67) (-1.70) (0.36) (1.69) (1.20) (0.89) Financial advice: Own judgement (2.35) (0.38) (0.94) (1.15) (4.67) (2.72) Own fin. jugdement bas. literacy (-1.91) (1.04) (-0.26) (-0.36) (-5.38) (-2.95) Higher vocal education (0.48) (0.16) (-0.30) (-0.05) (-1.12) (-0.58) Academic education (-0.18) (0.01) (-0.11) (-1.71) (-0.30) (-0.37) Age (-0.77) (0.20) (0.63) (1.20) (-0.53) (-0.72) Age (-0.29) (1.38) (2.03) (4.33) (1.40) (-0.53) Female (1.21) (1.39) (0.35) (2.75) (1.54) (0.82) Constant (2.21) (0.73) (1.13) (2.35) (3.42) (1.94) Observations Adjusted R Source: CentERpanel, Datastream, Euroinvestor, own calculations. See Section 2.3 for computational details. The OLS regression has been estimated on both waves of data and standard errors are clustered at the household level; the quantile estimates are based on a pure cross-section. All regressions use sampling weights. first group compared to the second group. Not doing so will reverse the order except for the highest quantiles. Table 4 presents the results of including the non-participants in the estimation sample, who have a return loss of zero. Remember from Section 2.4 that the quantiles under consideration need to be strictly positive for the estimator to be well-defined, so results of this exercise are presented in for every fifth percentile starting with the 75 th. Except for the female dummy, the estimates in the lower quantiles are all positive, albeit relatively small. This is an almost mechanical consequence of the different characteristics of participants and non-participants (compare the first and third column of Table 2). Unless someone invested in the efficient market portfolio directly, the return loss will be positive for participants. There does not seem to be any effect of financial literacy for those seeking others advice. The self-deciders with a financial literacy score of zero have consistently higher return losses at every quantile considered, reaching magnitudes of more than 100 basis points at the 95 th percentile. The interaction effect is small and mostly insignificant over the first 4 quantiles considered. It is back to the previous interpretation for the highest quintile. Interestingly, the education variables are positive over the entire distribution and significantly so in the lower part. The more educated invest more aggressively, but education does not lead to very efficient risk-taking. The same comment applies to the highest age group at each quantile under consideration, their return loss is substantially higher than that of the 19

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